AI 中文总结
该研究证明自由群的自由保测概率作用的轨道等价类含全弱混合作用，等价于特定代价的遍历可树化等价关系由自由全弱混合作用生成，解答了Miller与Tserunyan的问题。
AI 中文摘要
我们证明，自由群的每个自由保测概率（pmp）作用的轨道等价类都包含一个全弱混合作用。等价地，每个代价为$n\in\mathbf{N}\cup\{\infty\}$的遍历可树化pmp等价关系都由$\mathbf{F}_n$的一个自由全弱混合作用生成，这回答了Miller和Tserunyan提出的问题。证明通过考虑沿固定混合变换的边滑动的波兰空间，且对每个$w\neq e\in\mathbf{F}_n$，产生具有$w$弱混合性质的作用的边滑动集合是一个贫集。
英文摘要
We prove that the orbit equivalence class of every free ergodic probability-measure-preserving (pmp) action of a free group contains a totally weak mixing action. Equivalently, every ergodic treeable pmp equivalence relation of cost $n\in\mathbf{N}\cup\{\infty\}$ is generated by a free totally weak mixing action of $\mathbf{F}_n$. This answers a question of Miller and Tserunyan. The proof goes by considering a Polish space of edge slidings along a fixed mixing transformation and proving that for every $w\not=e\in\mathbf{F}_n$ the set of edge slidings that produce an action with $w$ weakly mixing forms a comeager set.
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